A bought 2 adult tickets and 3 children’s tickets for $44.50. B bought 3 adult tickets and 6 children’s tickets for $78. Find the price of an adult ticket and the price of a child’s ticket.

Question

SOMEBODY ANSWER NOW I NEED HELP AS FAST AS POSSIBLE!!!!!!!!

Answer 1

Let A = Price of ADULT ticket

Let C = Price of CHILD ticket

A: 2A + 3C = 44.5

B: 3A + 6C = 78

We have 2 LINEAR EQUATIONS with 2 VARIABLES.

Multiply -2 times the "A" equation, so when we add 6C to -6C, the "C's" cancel each other out.

-4A + -6C = -89

-4A - 6C = -89

Now ADD the 2 LINEAR EQUATIONS.

-4A - 6C = -89

3A + 6C = 78

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-A = - 11

Multiply above equation by negative one to make A and 11 positive.

A = $11

ADULT TICKETS COST $11

To determine the amount of CHILDREN tickets, plug in $11 for "A" in either one of the equations.

3A + 6C = 78

3(11) + 6C = 78

33 + 6C = 78

6C = 78 - 33 Subtracting 33 from both sides of the equation.

6C = 45

6C/6 = 45/6 Dividing both sides of the equation by 6.

C = $ 7.50

CHILDREN TICKETS COST $ 7.50

CHECKING: Plug in $11 for A and $7.50 for C in either of the 2 equations.

2A + 3C = 44.5 ?

2(11) + 3(7.5) = 22 + 22.5 = 44.5. YES!

Hope this was helpful SANAH.